2x(x-13)=32

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Solution for 2x(x-13)=32 equation: 


Simplifying
2x(x + -13) = 32

Reorder the terms:
2x(-13 + x) = 32
(-13 * 2x + x * 2x) = 32
(-26x + 2x2) = 32

Solving
-26x + 2x2 = 32

Solving for variable 'x'.

Reorder the terms:
-32 + -26x + 2x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + -26x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + -13x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-16 + -13x + x2)' equal to zero and attempt to solve:

Simplifying
-16 + -13x + x2 = 0

Solving
-16 + -13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -13x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -13x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -13x + x2 = 0 + 16
-13x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-13x + x2 = 16

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = 16 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 16 + 42.25

Combine like terms: 16 + 42.25 = 58.25
42.25 + -13x + x2 = 58.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 58.25

Calculate the square root of the right side: 7.632168761

Break this problem into two subproblems by setting 
(x + -6.5) equal to 7.632168761 and -7.632168761.


Subproblem 1
x + -6.5 = 7.632168761

Simplifying
x + -6.5 = 7.632168761

Reorder the terms:
-6.5 + x = 7.632168761

Solving
-6.5 + x = 7.632168761

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 7.632168761 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 7.632168761 + 6.5
x = 7.632168761 + 6.5

Combine like terms: 7.632168761 + 6.5 = 14.132168761
x = 14.132168761

Simplifying
x = 14.132168761


Subproblem 2
x + -6.5 = -7.632168761

Simplifying
x + -6.5 = -7.632168761

Reorder the terms:
-6.5 + x = -7.632168761

Solving
-6.5 + x = -7.632168761

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -7.632168761 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -7.632168761 + 6.5
x = -7.632168761 + 6.5

Combine like terms: -7.632168761 + 6.5 = -1.132168761
x = -1.132168761

Simplifying
x = -1.132168761


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.132168761, -1.132168761}
Solution
x = {14.132168761, -1.132168761}

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